Trajectory planning is crucial in the motion planning of robots, where finding the time-optimal path parameterization (TOPP) of a given path subject to kinodynamic constraints is an important component of trajectory planning. The tangential discontinuity at the intersection of continuous line segments limits the speed of trajectory planning and can easily cause jitter and over-constraint phenomena. Smooth transitions at corners can be achieved by inserting parameter spline curves. However, due to the insensitivity of parameter spline curves to arc length, their performance in the application of the TOPP algorithm, which relies on the higher-order robot kinematics smoothness (i.e., the function q(s) of the configuration space to the Cartesian space), fails to meet expectations.

中文翻译：

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S 型角度圆弧曲线：增强机器人时间最优路径参数化，实现高阶平滑运动


轨迹规划在机器人的运动规划中至关重要，其中寻找受运动动力学约束的给定路径的时间最优路径参数化（TOPP）是轨迹规划的重要组成部分。连续线段相交处的切向不连续性限制了轨迹规划的速度，并且很容易引起抖动和过约束现象。通过插入参数样条曲线可以实现拐角处的平滑过渡。然而，由于参数样条曲线对弧长不敏感，其在TOPP算法应用中的性能依赖于高阶机器人运动学平滑度（即配置空间的笛卡尔函数q(s)）空间），未能达到预期。